Julia Gillard was not across the details of climate change policy early in her prime ministership and should bear some responsibility for the demise of a price on carbon, Greens leader Christine Milne says.

Ms Milne said the former prime minister made a "disastrous" political decision when she conceded her carbon pricing scheme constituted a carbon tax.

The carbon price was abolished last Thursday with the support of all Senate crossbenchers, but the blame game over who brought it down continues. Last week, Labor senators tied the scheme's demise to the Greens' decision to vote against Kevin Rudd's Carbon Pollution Reduction Scheme in 2009.

"A fundamental error occurred when Julia Gillard went on television and conceded that an emissions trading scheme with a fixed price was a tax," Ms Milne told Sky News on Sunday. "That gave Tony Abbott everything he needed to ramp up his campaign on a tax.

"It was always about a carbon price and that concession to the idea of a tax was disastrous. I can't tell you [what I thought] when I saw that happening, unfolding in front of me."

Ms Milne said she believed Ms Gillard made the concession early in her prime ministership because she did not understand the crucial difference between a carbon tax and an emissions trading scheme.

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"She had opposed Kevin Rudd continuing with carbon pricing in early 2010 and I don't think she was across the policy detail," Ms Milne said.

Ms Gillard has acknowledged the decision not to contest the carbon tax label was a mistake.

"I feared the media would end up playing constant silly word games with me, trying to get me to say the word 'tax'," she said in an article for The Guardian last September.

"I wanted to be on the substance of the policy, not playing 'gotcha'. But I made the wrong choice and, politically, it hurt me terribly."

The Gillard government's carbon pricing scheme included a three-year fixed price period before moving to a flexible price from July 2015. Mr Rudd's CPRS – commonly known as an emissions trading scheme – included a fixed price for one year.

Ms Milne maintained the Greens were right to block Labor's CPRS in 2009. Because of the scheme's generous handouts to polluters, the CPRS was a "dog of a policy" and "worse than nothing", she said.

Opposition Leader Bill Shorten has said Labor will take an emissions trading scheme to the next election – a policy the Abbott government insists would amount to a reintroduction of the carbon tax.

Coalition House leader Christopher Pyne told Mr Shorten in Parliament last week the government would "hang this around his neck like a rotten, stinking carcass right through to election day".

"We can now tell the Australian public with great confidence that if they vote Labor at the next election the carbon tax will be reintroduced," he said.